Tag: statistics

The Limits of Conspiracy Debunking—Revisited

Posted on by David Kordahl

by David Kordahl

The sides of a Roman die (image from Wikipedia).

Note: This piece is an accidental addendum to my column of March 2021, “The Limits of Conspiracy Debunking,” though it can be read separately.

Sometimes, we’re surprised. Though everyday surprises can be comedic, the surprises that we register collectively are more often tragic. My parents both remember the assassination of John F. Kennedy as one of the most shocking events of their childhoods. I suppose the attacks on the World Trade Center and the Pentagon on September 11, 2001, constitute the most shocking of mine. Both the JFK assassination and the 9/11 attacks have attracted conspiracy speculation ever since they occurred. And there are good reasons for this, I contend, even if no conspiracies were involved.

Collective feelings of surprise, of widespread shock, reflect a vague feeling that such events were unlikely, though their very unlikeliness makes their odds hard to calculate. In such cases, alternative explanations—“conspiracy theories,” if you’re feeling ungenerous—seem attractive because they change our estimated likelihoods for surprising events. After these events, it’s natural enough to ask, Why didn’t I see that coming? We might consider, with some shame, whether our expectations should have included wider possibilities, so we might have been less surprised.

After such shocks, the prophets who forewarned disaster gain legitimacy. People retrospectively consider alternatives that accommodate their prior surprise. This rethinking serves to change their subjective odds for the likelihood of the original event. But that’s a problem, if we’re interested in any sort of self-consistency, since this retrospective modulation of odds is only reasonable if we actually should not have been surprised.

This may all sound circular, but there’s a solution at hand. If unique events can be reclassified as non-unique, we can move away from seeing events as being unprecedented, and statistics will once again apply. Returning to shocking events, JFK might be rolled into the category of “political assassinations,” and 9/11 into the category of “political terrorism,” and we might then think through the odds by examining trends in those categories. Read more »

Football, Finance, and Surprises

Posted on by Nick Werle

As the New Orleans Saints lined up to kick off the second half of Super Bowl XLIV, CBS Sports color commentator and former Super Bowl MVP Phil Simms was explaining why the Saints should have deferred getting the ball after winning the pregame coin toss. Simms suggested that the Saints, 4½-point underdogs to the Indianapolis Colts, would be in a better position were they not giving the ball to future Hall of Fame quarterback Peyton Manning, who already enjoyed a four-point lead and had had 30 minutes to study the Saints’ defensive strategy. Simms had barely finished this thought when Saints’ place kicker Thomas Morstead surprised everyone – the 153.4 million television viewers, the 74,059 fans in attendance, and most importantly the Indianapolis Colts – with an onside kick. The ball went 15 yards, bounced off the facemask of an unprepared Colt, and was recovered by the Saints, who took possession of the ball and marched 58 yards down the field to score a touchdown and gain their first lead of the game, 13-10. The Saints would go on to win the championship in an upset, 31-17.

Although Saints quarterback Drew Brees played an outstanding game and the defense was able to hold a dangerous Indianapolis team to only 17 points, Head Coach Sean Payton received the bulk of the credit for the win, in large part because of his daring call to open the second half. Onside kicks are considered risky plays and usually appear only when a team is desperate, near the end of a game. In fact the Saints’ play, code named “Ambush,” was the first onside kick attempted before the fourth quarter in Super Bowl history. And this is precisely why it worked. The Colts were completely surprised by Payton’s aggressive play call. Football is awash in historical statistics, and these probabilities guide coaches’ risk assessments and game planning. On that basis, didn’t Indianapolis Head Coach Jim Caldwell have zero reason to prepare his team for an onside kick, since the probability of the Saints’ ambush was zero (0 onside kicks ÷ 43 Super Bowl second halves)? But if the ambush’s probability was zero, then how did it happen? The answer is that our common notion of probability – as a ratio of the frequency of a given event to the total number of events – is poorly suited to the psychology of decision making in advance of a one-time-only situation. And this problem is not confined to football. Indeed, the same misunderstanding of probability plagues mainstream economics, which is stuck in a mathematical rut best suited to modeling dice rolls.

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Statistics – Destroyer of Superstitious Pretension

Posted on by Tauriq Moosa

Statistics-education-research-day1 In Philip Ball’s Critical Mass: How One Thing Leads to Another, he articulates something rather profound: statistics destroys superstition. The idea, once expressed, is simple but does not stem its profundity. Incidents in small numbers sometimes become ‘miraculous’ only because they appear unique, within a context that fuels such thinking. Ball’s own example is Uri Geller: in the 1970’s, the self-proclaimed psychic stated he would stop the watches of several viewers. He, perhaps, twisted his face and furrowed his brow and all over America watches stopped. America, no doubt, turned into an exclamation mark of incredulity. What takes the incident out of the sphere of the miraculous, however, is the consideration of statistics: With so many millions of people watching, what was the likelihood of at least some people’s watches stopping anyway? What about all those watches that did not stop?

Our psychological make-up seeks a chain in disparate events. Our mind is a bridge-builder across chasms of unrelated incidents; a credulity stone-hopper, crouching at each juncture awaiting the next link in a chain of causality. To paraphrase David Hume, we tend to see armies in the clouds, faces in trees, ghosts in shadows, and god in pizza-slices.

Many incidents that people refer to as miraculous, supernatural, and so on, become trivial when placed within their proper context. Consider the implications of this: Nicholas Leblanc, a French chemist, committed suicide in 1806; Ludwig Boltzmann, the physicist who explained the ‘arrow of time’ and gave us the Boltzmann Constant, committed suicide in 1906; his successor, Paul Ehrenfest, also committed suicide, in 1933; the American chemist Wallace Hume Carothers, credited with inventing Nylon, killed himself in 1937. This seems to ‘imply’ a strong link between suicide and science. Of course, as Ball indicates himself, we must look at the contexts: We must ask what the suicide-rating of these different demographics was in general: of Americans, Europeans, males, and any other demographic.

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